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Inequalities (Pos/Neg): Is x less than y ?

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by II » Sun Mar 23, 2008 4:58 pm
Is x less than y ?

(1) 2x is less than 3y

(2) xy is greater than 0.

Interested in your logic in solving this question.

Thanks in advance.
Last edited by II on Mon May 05, 2008 1:47 am, edited 2 times in total.
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Re: Inequalities ...

by Stuart@KaplanGMAT » Mon Mar 24, 2008 11:12 am
II wrote:Is x less than y ?

(1) 2x is less than 3y

(2) xy is greater than 0.

Interested in your logic in solving this question.

Thanks in advance.
(1) 2x < 3y

Let's pick numbers to see if we can get a yes and a no:

x = 1 y=20 (2 < 60)
Is 1 < 20? YES

x=2.5 y=2 (5 < 6)
Is 2.5 < 2? NO

YES and NO: insufficient.

(2) xy > 0

i.e. x and y are either both negative or both positive.
No info about values: insufficient.

Combined:

The numbers we chose for (1) are all positive, so they also follow (2). Therefore, we can pick the same numbers and still get a YES and a NO: not enough information, choose (E).
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by II » Mon Mar 24, 2008 2:20 pm
Thanks Stuart. This was also the approach I used.
Is there another approach to solve this, apart from plugging-in numbers ?

Thanks.
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by cjiang16 » Mon Apr 07, 2008 11:22 pm
:D
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by codesnooker » Tue Apr 08, 2008 12:12 am
II wrote: Is there another approach to solve this, apart from plugging-in numbers ?
Here is the another solution:-

Statement 1: 2X < 3Y

Now analyze this above statement....

X/Y <3/2

X/Y < 1.5

It means that X/Y could be greater than 1 also but always less than 1.5

To make X/Y >= 1, the Y should either be equal to X or less than X.

In other words, X could be less Y only in case X/Y < 1.

So statement 1 would be insufficient.

For statement 2 and combined, its simple as explained by Stuart.
Stuart wrote:(2) xy > 0

i.e. x and y are either both negative or both positive.
No info about values: insufficient.

Combined:

The numbers we chose for (1) are all positive, so they also follow (2). Therefore, we can pick the same numbers and still get a YES and a NO: not enough information, choose (E).
Hope it makes sense :D
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Re: Inequalities ...

by KICKGMATASS123 » Thu May 21, 2009 4:15 pm
Stuart Kovinsky wrote:
II wrote:Is x less than y ?

(1) 2x is less than 3y

(2) xy is greater than 0.

Interested in your logic in solving this question.

Thanks in advance.
(1) 2x < 3y

Let's pick numbers to see if we can get a yes and a no:

x = 1 y=20 (2 < 60)
Is 1 < 20? YES

x=2.5 y=2 (5 < 6)
Is 2.5 < 2? NO

YES and NO: insufficient.

(2) xy > 0

i.e. x and y are either both negative or both positive.
No info about values: insufficient.

Combined:

The numbers we chose for (1) are all positive, so they also follow (2). Therefore, we can pick the same numbers and still get a YES and a NO: not enough information, choose (E).
FOR STATEMENT 1 HOW DO YOU KNOW YOU IF YOU CAN ONLY PICK POSITIVE NUMBERS? HOW DO YOU DETERMINE THAT?
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Re: Inequalities ...

by aj5105 » Thu May 21, 2009 8:15 pm
We can pick any number with any sign we want to as long as the stem condition and condition in statement (1) are satisfied.

x < y : YES

x > y : NO


2x < 3y

2*1/2 < 3*1 (Considering x = 1/2 and y = 1 : YES)

2*1 < 3*1 (Considering x = 1 and y = 1 : NO)


KICKGMATASS123 wrote:
Stuart Kovinsky wrote:
II wrote:Is x less than y ?

(1) 2x is less than 3y

(2) xy is greater than 0.

Interested in your logic in solving this question.

Thanks in advance.
(1) 2x < 3y

Let's pick numbers to see if we can get a yes and a no:

x = 1 y=20 (2 < 60)
Is 1 < 20? YES

x=2.5 y=2 (5 < 6)
Is 2.5 < 2? NO

YES and NO: insufficient.

(2) xy > 0

i.e. x and y are either both negative or both positive.
No info about values: insufficient.

Combined:

The numbers we chose for (1) are all positive, so they also follow (2). Therefore, we can pick the same numbers and still get a YES and a NO: not enough information, choose (E).
FOR STATEMENT 1 HOW DO YOU KNOW YOU IF YOU CAN ONLY PICK POSITIVE NUMBERS? HOW DO YOU DETERMINE THAT?
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